I know that this is late to the party. However, what I would do is wait a couple of years before replaying Pokemon Black. It's only been two years, and the sequel was the just released last year around the same time that was almost exactly the same. Around this time, I would play generation four games like Diamond, Pearl, and Platinum. To me, it doesn't feel right to play Heartgold, Soulsilver, and the generation five games because they feel too new. This is my opinion, and that's what I did with Pokemon Red and Pokemon Leafgreen. I replayed Red in 2007 and replayed it again two years ago. Leafgreen, I replayed in 2008.

I'm tempted to restart Pearl at some point (as I don't think I've played it in a few years), but I think I have an event Pokemon (Jirachi) on it so that's the only reason I don't want to just wipe it. Possibly I have something on my HeartGold as well (I kind of remember some sort of GameStop event going on at launch, but I forgot what it was). I think I backed up my Pearl save with an AR. Is that enough to avoid worry about losing the (legitimately) irreplaceable data? Unsure about HG.
Or else if I have a 3DS and a DS as well as a White 2, I should at some point be able to use both to transfer the rare Pokemon for storage?